Dimkid: SVD Combining Age Groups

In this document, I explore how children’s use of “modes” differs across age groups. I focus here on Approach #1 from svd_approaches.Rmd: No mean-centering, characters as rows and capacities as columns.

I try out 2 different methods for combining these age groups:

1. Treat the evaluations of a given character by each of the two age groups as if they were distinct “characters,” yielding 18 total characters instead of 9.
2. Treat the evaluations of a given capacity by each of the two age groups as if they were distinct “capacities,” yielding 40 total capacities instead of 20.

It will be important to think through this using other “Approaches” (see svd_approaches.Rmd); this is a starting point.

As a reminder, in this study, 123 7- to 9-year-old and 124 4- to 6-year-old US children rated 9 characters (between-subjects) on 20 capacities (within subjects). (See Weisman, Dweck, & Markman, 2018, Proc. CogSci.)

Combination Method #1

Raw data matrix visualizations

Joining, by = c("character", "anger", "awareness", "choice", "depth", "embarrassment", "fatigue", "fear", "figuring_out", "guilt", "happiness", "hunger", "hurt_feelings", "love", "memory", "nausea", "pain", "pride", "sadness", "smell", "temperature")

SVD

Reconstructed data

Feature vectors

Singular values

Item vectors

Plotting in dimensions

Joining, by = "item"
Column `item` joining factor and character vector, coercing into character vector

Joining, by = "item"
Column `item` joining factor and character vector, coercing into character vector

Joining, by = "item"
Column `item` joining factor and character vector, coercing into character vector

Ignoring unknown aesthetics: x, y, label

Ignoring unknown aesthetics: x, y, label

Ignoring unknown aesthetics: x, y, label

Combination Method #2

Raw data matrix visualizations

Joining, by = c("character", "capacity", "mean_rating")

SVD

Reconstructed data

Feature vectors

Singular values

Item vectors

Plotting in dimensions

Joining, by = "item"
Column `item` joining factor and character vector, coercing into character vector

Joining, by = "item"
Column `item` joining factor and character vector, coercing into character vector

Joining, by = "item"
Column `item` joining factor and character vector, coercing into character vector

Ignoring unknown aesthetics: x, y, label

Ignoring unknown aesthetics: x, y, label

Ignoring unknown aesthetics: x, y, label